This invention relates to a state observer for a permanent magnet or wound rotor synchronous motor.
Electric motors are traditionally used as actuators. However, they may also be used as sensors of the motion they actuate. This simultaneous operation as an actuator and sensor can be beneficial when additional motion sensors are too expensive, large, unreliable, or otherwise undesirable. In particular, the potential cost savings of eliminating a motion sensor can be great.
An electric motor can be successfully used as a sensor of its own motion because this motion effects the voltages and currents in it. Thus, the voltages and currents possess information concerning the motion. What is needed, then, is a means of extracting this information so as to estimate the desired motion. Some form of signal processing is necessary, which places additional demands on the control electronics. However, as digital processors continue to become faster and less expensive, this additional signal processing becomes less of a burden.
In this specification, an identity state observer is used to estimate the electrical and mechanical states of a smooth rotor permanent magnet synchronous motor. The estimated states are the direct and quadrature currents, the rotor velocity, and the rotor position. Thus, the output of the observer is precisely the states desired for typical implementations of field-oriented, or vector, control [5]. (Numbers in brackets refer to the references listed at the end of this specification.) An identity state observer utilizes a model of the dynamics of the machine observed and includes an innovation term multiplied by a gain. By "smooth rotor" is meant a machine having a single harmonic of air gap flux.
The estimation of motor motion using measurements of electrical variables is not a new idea. A wide variety of methods have already been investigated in the literature. At one extreme are waveform detection methods that are commonly associated with permanent-magnet and variable reluctance stepper motors; see references in [6]. These methods attempt to identify specific events such as peaks or zero crossings in the electrical waveforms that are the result of the back-emf of the rotating rotor. They have been successfully demonstrated for commutation needs, and may be implemented using inexpensive electronics, which is advantageous from a manufacturing viewpoint. However, they are not as accurate as possible because they do not utilize all the information present in the waveforms. The fact that the back-emf is always present while the rotor is moving means that back emf information which may reveal the position of the rotor is always present in the waveforms.
One way to extract all the information in the waveforms is to model the dynamics of the motor, drive these dynamics with the same input as is used to drive the real motor, and somehow ensure that errors between the modeled motor and real motor are minimized. If this can be done, then the states of the modeled motor will effectively summarize all the information in the waveforms up to the present time, and the model will accurately reflect the behavior of the real motor. In a state observer, an output is defined as a combination of the states and this output is compared with the equivalent measured output of the real motor. Any error between the two signals is then used to correct the state trajectory of the observer.
State observers have been studied for a wide variety of electric machines. For example, a linear observer based on the linearized model of a generator is studied in [8]. Although the observer is designed for operation at a specific operating point, it is shown that it performs satisfactorily for small perturbations over a wide range of operating conditions.
In [6] and in U.S. patent application Ser. No. 927,532, filed Nov. 5, 1986, an observer is developed for a variable reluctance motor where spatial variations in phase inductances affect the evolution of the flux in the phases as the rotor rotates. An observer is constructed that models the spatially-varying motor dynamics, and a very accurate position estimate is produced under a constant speed assumption. The structure of this observer is nonlinear since the motor dynamics and the feedback gain on the innovation are nonlinear functions of the estimated states.
In [10], an observer for a synchronous generator that has the structure of a linear observer, that is, constant gains on linear innovation, is applied to a nonlinear model. A potential drawback is that the observer in [10] does not exploit the unique qualities of the nonlinearities in the generator, and therefore misses the potential for even faster converging estimates.
A complex observer strcture may be found in [2]. There, optimal control theory is used to develop an observer which is optimal with respect to random system noise and random measurement noise. The system noise may be due either to modeling errors or disturbances. Though not deemed as such in the paper, the resulting observer may be called an invariant embedded observer. It is similar to an extended Kalman filter and, unfortunately, appears to have many of the same drawbacks as the extended Kalman filter, particularly the necessity of carrying along a system of covariance dynamics which increasese the order of the observer from four to fourteen. Although optimization with respect to system noise is clearly desirable, it incurs a heavy price. No consideration is made of the underlying nonlinear system. Rotating machines have strong symmetries that can be exploited to yield simpler structures. The invariant embedded observer would have to be demonstrably superior to other methods before it could be seriously considered for real-time application.
Models for alternating current motors are nonlinear and estimation theory for nonlinear systems is not well developed compared to the wealth of guidance available for linear systems, such as direct-current motors. However, there is considerable symmetry in alternating-current motor models which can be used to simplify an estimation problem. Ignoring this symmetry may lead to estimators that are more complex than necessary. The state observer according to the invention combines the ideas of a linear observer with the d.sub.q transformation that may be applied to smooth-rotor machines. The resulting state observer is one that could not have been developed from a general expression for a nonlinear system.